[Fluide visqueux dans un domaine de faible épaisseur vérifiant la condition de glissement sur une frontière lègèrement rugueuse]
On considère un fluide visqueux de faible épaisseur ε sur un fond rugueux , périodique de période et amplitude , , où on impose la condition de glissement. Quand ε converge vers zéro on obtient un système de type Reynolds qui dépend de la limite λ de . Si , le fluide se comporte comme si on aurait imposé la condition d'adhérence sur . Ceci justifie la condition usuelle pour un fluide visqueux. Si le fluide se comporte comme si était plate. Enfin, pour , tout se passe comme si était plate, mais avec un coefficient de frottement plus élevé.
We consider a viscous fluid of small height ε on a periodic rough bottom of period and amplitude , , where we impose the slip boundary condition. When ε tends to zero we obtain a Reynolds system depending on the limit λ of . If , the fluid behaves as if we would impose the adherence condition on . This justifies why this is the usual boundary condition for viscous fluids. If the fluid behaves as if was plane. Finally, for it behaves as if was flat but with a higher friction coefficient.
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Juan Casado-Díaz 1 ; Manuel Luna-Laynez 1 ; Francisco Javier Suárez-Grau 1
@article{CRMATH_2010__348_17-18_967_0, author = {Juan Casado-D{\'\i}az and Manuel Luna-Laynez and Francisco Javier Su\'arez-Grau}, title = {A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary}, journal = {Comptes Rendus. Math\'ematique}, pages = {967--971}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.07.023}, language = {en}, }
TY - JOUR AU - Juan Casado-Díaz AU - Manuel Luna-Laynez AU - Francisco Javier Suárez-Grau TI - A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary JO - Comptes Rendus. Mathématique PY - 2010 SP - 967 EP - 971 VL - 348 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2010.07.023 LA - en ID - CRMATH_2010__348_17-18_967_0 ER -
%0 Journal Article %A Juan Casado-Díaz %A Manuel Luna-Laynez %A Francisco Javier Suárez-Grau %T A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary %J Comptes Rendus. Mathématique %D 2010 %P 967-971 %V 348 %N 17-18 %I Elsevier %R 10.1016/j.crma.2010.07.023 %G en %F CRMATH_2010__348_17-18_967_0
Juan Casado-Díaz; Manuel Luna-Laynez; Francisco Javier Suárez-Grau. A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 967-971. doi : 10.1016/j.crma.2010.07.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.023/
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